Multivariate GARCH models constitute the workhorse of empirical applications in several elds, a notable example being nancial econometrics. Unfortunately, ML (or quasi-ML) estimation of such models, although relatively straightforward in theory, is often made dicult by the fact that available software relies on numerical methods for computing the rst derivatives of the log-likelihood; the fact that these models often include several dozens of parameters makes it impractical to estimate even medium-sized models. In this paper, closed-form expressions for the score of the BEKK model of Engle and Kroner (1995) are obtained, and strategies for ecient computation are discussed.
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